Please post DDL, so that people do not have to guess what the keys, constraints, Declarative Referential Integrity, data types, etc. in your schema are. Learn how to follow ISO-11179 data element naming conventions and formatting rules. Temporal data should use ISO-8601 formats. Code should be in Standard SQL as much as possible and not local dialect.
This is minimal polite behavior on SQL forums. What little you did post is wrong. Rows are not records. Columns are not fields. Tables have no ordering. This is in the first 1-3 chapters of any book on RDBMS.
The MS proprietary IDENTITY table property (it is not a column) cannot be a valid by definition. Since we do not do math on identifiers, they are seldom (if ever!) a numeric in a properly designed schema.
You can use a function call
ROW_NUMBER() OVER (ORDER BY something_id) AS sticky_seq
This will always be correct, not waste disk space, etc. Now, if you had a Netflix queue and anted to re-arrange it, that is a different problem.
First of all I personally do not like to delete rows unless it is absolutely necessary for just this reason. I simply mark the row as deleted and exclude it from my queries so that the data is always there and prevent parent child orphan relation problems down the road. After all Disk Space is free these days and it is better to keep the data then to get rid of it.
What is Stick ID used for? Is this a label that sows in some report some were or is it a foreign key? I agree with Celko that we need you DDL so we can see what the data elements are.
Are you going to be doing this renumbering in a trigger of some kind? If so do you already have an update trigger and if you do can you post it?